Dark foreground, light background

I was photographing my girlfriend this weekend at the Jefferson memorial, around 2pm. The sun was positioned brightly, above and behind us and I was trying to take a picture of her leaning against a column, facing out towards the Washington monument. We were trying to recreate a photo captured of her grandmother standing in the same spot some 20-30 years earlier. The older picture was clearly done at a different time of the day - closer to high-noon, or the morning and in the late summer.

The issue that she was cast in shadow AND wearing almost all black, while the landscape behind her was all very bright sun-lit blue water, sky, etc. Because of this, I would get one of two images - either her well-lit and the background whited-out, or her in complete darkness, and the background pretty.

I've read about creating two exposures and combining them, but I'm not 100% clear on how the camera is giving me one exposure vs. the other (nor do I carry a tripod with me). For instance, if I removed her from the scene entirely, the image would always come out excellent - both foreground and background in wonderful color.

I have a Nikon D5100 with an 18-135mm lens. I also tried with my 35mm. I tried tons of different settings, including the auto-contrasting and auto-braketing settings, but always got the same results.

I'd prefer to not post her picture here. I did an image search on google and this is the closest I could find to the composition we were doing, only zoomed a bit more in, where only a sliver of the left column was in view: